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Chapter 13: Q 72. (page 1068)

Let bbe a constant. Prove that the equation of the plane y=bisr=bcsc蠁csc胃in spherical coordinates.

Short Answer

Expert verified

This is proved using relationx=rsin蠒cos胃,y=rsin蠒sin胃,z=rcos蠒.

Step by step solution

01

Given Information

Equation of rectangular coordinates is given as y=b (bis constant).

02

Simpification

We know that

x=rsin蠒cos胃,y=rsin蠒sin胃,z=rcos蠒

For conversion of given equation of plane to spherical coordinates, use y=rsin蠒sin胃in given equation

rsin蠒sin胃=b

鈬�r=bsin蠒sin胃

=b1sin蠒1sin胃

role="math" localid="1652391295106" r=bcsc蠒csc胃

Hence proved.

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